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A Wiener–Kolmogorov Filter for Seasonal Adjustment and the Cholesky Decomposition of a Toeplitz Matrix

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  • D. Stephen G. Pollock

    (University of Leicester)

  • Emi Mise

    (University of Leicester)

Abstract

A flexible method for removing the seasonal fluctuations from economic data is described. It can be used to remove not only the elements at the seasonal frequencies but also the adjacent elements, which may contribute significantly to the seasonal fluctuations but which are liable to be only mildly attenuated by the usual filters. The method has been implemented in a computer program, SEADOS, which, together with its accompanying manual, is available at the address http://www.sigmapi.org.uk/seados.zip/ . The program employs a specialised version of a Cholesky decomposition, which is adapted to the case of a narrow-band Toeplitz matrix, in which each band contains a unique repeated element and where the number of bands is considerably less than the order of the matrix, which is assumed to be large. The Pascal code of this algorithm is presented here together with that of some accompanying procedures.

Suggested Citation

  • D. Stephen G. Pollock & Emi Mise, 2022. "A Wiener–Kolmogorov Filter for Seasonal Adjustment and the Cholesky Decomposition of a Toeplitz Matrix," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 913-933, March.
    • Handle: RePEc:kap:compec:v:59:y:2022:i:3:d:10.1007_s10614-020-10087-1
    DOI: 10.1007/s10614-020-10087-1
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    References listed on IDEAS

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    1. [Reference to Proietti], Tommaso, 2000. "Comparing seasonal components for structural time series models," International Journal of Forecasting, Elsevier, vol. 16(2), pages 247-260.
    2. McElroy, Tucker, 2008. "Matrix Formulas For Nonstationary Arima Signal Extraction," Econometric Theory, Cambridge University Press, vol. 24(4), pages 988-1009, August.
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